Question

Szybko 2 proste zadania o logarytmach!!! czekam do 22;00!!! ;)

dam naj.

Answer 1

ZADANIE 2.30

 kiedy nie ma żadnej podstawy to wynosi ona 10

A)

log₁₀4+log₁₀25=log₁₀(4*25)=log₁₀100=2       

(bo 10²=100)

 

B)

log₁₀50+log₁₀20=log₁₀(50*20)=log₁₀1000=3    

(bo 10³=1000)

 

C)

log₆2+log₆18=log₆(2*18)=log₆36=2

(bo 6²=36)

 

D)

log₂96-log₂6=log₂(96:6)=log₂16=4              

(bo 2⁴=16)

 

E)

log₉108-log₉4=log₉(108:4)=log₉27=3/2

(bo 9 do potęgi 3/2=√9³=3³=27

 

F)

log½6-log½3=log½(6:3)=log½2= -1

(bo (1/2)⁻¹=2)

 

G)

log₁₀6-log₁₀2-log₁₀3=log₁₀(6:2)-log₁₀3=log₁₀3-log₁₀3=log₁₀(3:3)=log₁₀1=0  

(bo 10⁰=1)

 

H)

log₄480-log₄5-log₄3=log₄(480:5)-log₄3=log₄96-log₄3=log₄(96:3)=log₄32=5/2

(bo 4 do potęgi 5/2=√4⁵=2⁵=32

 

ZADANIE 2.31

A)

2log₃6-log₃4=log₃(6²:4)=log₃(36:4)=log₃9=2

(bo 3²=9)

 

B)

log₁₀8+3log₁₀5=log₁₀(8*5³)=log₁₀(8*125)=log₁₀1000=3

(bo 10³=1000)

 

C)

log₄3+2log₄ 2√3/3=log₄3+log₄(2√3/3)²=log₄3+log₄ 12/9=log₄(3*12/9)=log₄4=1

(bo 4¹=4)

 

D)

2log½5+4log½2-2log½10=log½(5²*2⁴)-log½10²=log½400-log½100=log½(400:100)=

log½4= -2

(bo 1/2⁻²=2²=4)

 

E)

log₃3-3log₃2+log₃24=log₃(3:2³)+log₃24=log₃3/8+log₃24=log₃(3/8*24)=log₃9=2

 

F)

log¼18+log¼8-2log¼3=log¼(18*8:9)=log¼16= -2

 

G)

log₁₀15+log₁₀2+2log₁₀5-log₁₀3/4=log₁₀(15*2*25:3/4)=log₁₀1000=3